An approximation algorithm for parallel machine scheduling with simple linear deterioration

Ren, Chuan-rong; Kang, Liying

doi:10.1007/s11741-007-0406-3

Cited by 9 publications

(2 citation statements)

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“…Another research stream addresses the parallel machine problem when p' j = b j e j , in other words, eliminates the constant 'baseline' portion of the processing time. Ren and Kang (2007) present polynomial approximation algorithms for the makespan minimization problem and provide the complexity of the two machine case. Ji and Cheng (2008) solve the sum of job completion times problem, while Ji and Cheng (2009) address the makespan and sum Figure 1.…”

Section: Literature Reviewmentioning

confidence: 99%

Maximizing the Percentage of On-Time Jobs with Sequence Dependent Deteriorating Process Times

Ruíz-Torres

Paletta

2015

International Journal of Operations Research and Information Systems

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The paper addresses the problem of maximizing the percentage of on-time jobs in a parallel machine environment with sequence dependent deterioration. The deterioration of each machine (and therefore of the job processing times) is a function of the sequence of jobs that have been processed by the machine. Two machine loading strategies are combined with a set of list scheduling algorithms to solve the identical and unrelated machine versions of the problem. The proposed solutions approaches are tested using a large set of problem instances that consider various levels of the number of jobs and machines, the due date tightness, and the deterioration effect. The results indicate that the approach based on loading considering all machines simultaneously and assigns jobs by due date is the most effective.

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Section: Literature Reviewmentioning

confidence: 99%

Maximizing the Percentage of On-Time Jobs with Sequence Dependent Deteriorating Process Times

Ruíz-Torres

Paletta

2015

International Journal of Operations Research and Information Systems

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“…Kang and Ng [13] proposed an FPTAS. For simple linear deterioration, Kononov [14] and Mosheiov [22] independently showed that the problem is NPhard, and Ren and Kang [26] proposed an FPTAS.…”

Section: Introductionmentioning

confidence: 99%

Online Makespan Scheduling of Linear Deteriorating Jobs on Parallel Machines

Ojiaku

Wong

et al. 2012

Lecture Notes in Computer Science

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Abstract. Traditional scheduling assumes that the processing time of a job is fixed. Yet there are numerous situations that the processing time increases (deteriorates) as the start time increases. Examples include scheduling cleaning or maintenance, fire fighting, steel production and financial management. Scheduling of deteriorating jobs was first introduced on a single machine by Browne and Yechiali, and Gupta and Gupta independently. In particular, lots of work has been devoted to jobs with linear deterioration. The processing time pj of job Jj is a linear function of its start time sj, precisely, pj = aj + bjsj, where aj is the normal or basic processing time and bj is the deteriorating rate. The objective is to minimize the makespan of the schedule.We first consider simple linear deterioration, i.e., pj = bjsj. It has been shown that on m parallel machines, in the online-list model, LS (List Scheduling) is (1 + bmax) 1− 1 m -competitive. We extend the study to the online-time model where each job is associated with a release time. We show that for two machines, no deterministic online algorithm is better than (1 + bmax)-competitive, implying that the problem is more difficult in the online-time model than in the online-list model. We also show that LS is (1 + bmax)) -competitive, meaning that it is optimal when m = 2. IntroductionMakespan scheduling of deteriorating jobs. Scheduling jobs (with fixed processing time) on single or parallel machines is a classical problem [24]. Yet, there are numerous situations that the processing time increases (deteriorates) as the start time increases. For example, to schedule maintenance or cleaning, a delay often requires additional efforts to accomplish the task. Other examples are found in fire fighting, steel production and financial management [15,21] . Since then, the problem has attracted a lot of attention, and has been studied in other time dependent models. Comprehensive surveys can be found in [1,6,9], which also discussed other objective functions. Linear deterioration. We focus on jobs with linear deterioration, which has been studied in more detail due to its simplicity while capturing the essence of real life situations. The processing time of a job is a monotone linear function of its start time. Precisely, the processing time p j of a job J j is expressed as p j = a j + b j s j , where a j ≥ 0 is the "normal" or "basic" processing time, b j > 0 is the deteriorating rate, and s j is the start time. As the start time gets larger, the actual processing time also gets larger.Linear deterioration is further said to be simple if a j = 0, i.e., p j = b j s j . In this case, in order to avoid trivial solution, it is natural to assume that the start time of the first job is t 0 > 0 since a start time of zero means that the processing time of all jobs is zero. Mosheiov [20,21] justified simple linear deterioration as follows: as the number of jobs increases, the start time of jobs gets larger, and the actual processing time of infinitely many jobs is no longer aff...

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Multiobjective approach for deteriorating jobs scheduling for a sustainable manufacturing system

Tigane

Dahane

Boudhar

2018

Int J Adv Manuf Technol

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An approximation algorithm for parallel machine scheduling with simple linear deterioration

Cited by 9 publications

References 11 publications

Maximizing the Percentage of On-Time Jobs with Sequence Dependent Deteriorating Process Times

Maximizing the Percentage of On-Time Jobs with Sequence Dependent Deteriorating Process Times

Online Makespan Scheduling of Linear Deteriorating Jobs on Parallel Machines

Multiobjective approach for deteriorating jobs scheduling for a sustainable manufacturing system

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